Problem: Which of these numbers is prime? ${51,\ 69,\ 72,\ 79,\ 81}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 51 are 1, 3, 17, and 51. The factors of 69 are 1, 3, 23, and 69. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. The factors of 79 are 1 and 79. The factors of 81 are 1, 3, 9, 27, and 81. Thus, 79 is a prime number.